Bearing assemblies, apparatuses, and related methods of manufacture

ABSTRACT

In an embodiment, a bearing assembly may include a support ring to which one or more superhard bearing elements may be mounted. The support ring may include one or more relief features configured to reduce residual stresses in the superhard bearing elements that are induced by brazing the superhard bearing elements to the support ring, operational loads, other processes, or combinations of the foregoing. Reducing the residual stresses in the superhard bearing elements may help prevent damage to the superhard bearing elements. The bearing assembly may be used in subterranean drilling systems and/or other types of systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/675,323 filed on 31 Mar. 2015, which is a continuation of U.S.application Ser. No. 13/241,412 filed on 23 Sep. 2011 (now U.S. Pat. No.9,016,405 issued on 28 Apr. 2015), which is a continuation-in-part ofU.S. application Ser. No. 12/854,337 filed on 11 Aug. 2010 (now U.S.Pat. No. 8,800,686 issued on 12 Aug. 2014), the contents of which areincorporated herein, in their entirety, by this reference.

BACKGROUND

Subterranean drilling systems that employ downhole drilling motors arecommonly used for drilling boreholes in the earth for oil and gasexploration. Subterranean drilling systems typically include a housingenclosing a downhole drilling motor operably connected to an outputshaft. One or more thrust-bearing apparatuses may also be operablycoupled to the downhole drilling motor for carrying thrust loadsgenerated during drilling operations. A rotary drill bit may also beconnected to the output shaft and be configured to engage a subterraneanformation and drill a borehole. As the borehole is drilled with therotary drill bit, pipe sections may be connected to the subterraneandrilling system to form a drill string capable of progressively drillingthe borehole to a greater size or depth within the earth.

Each bearing apparatus may include a stator that does not rotate and arotor that is attached to the output shaft and rotates with the outputshaft. The stator and rotor may each include a plurality of superhardbearing elements or inserts. Each superhard bearing element may befabricated from a polycrystalline diamond compact (“PDC”) that providesa bearing surface that bears against other bearing surfaces during use.

In a conventional PDC bearing apparatus, a bearing assembly may includea support ring that includes recesses configured to accept the superhardbearing elements. The superhard bearing elements may be partiallydisposed in the recesses of the support ring and secured partiallytherein via brazing or other processes. However, heating and/or coolingfrom brazing and other processes may generate significant residualstresses in the superhard bearing elements. These residual stressesalone and/or in combination with operational loads may cause fracturingand/or weakening of the superhard bearing elements which may result infailure of bearing assemblies and/or bearing apparatuses.

Therefore, manufacturers and users of bearing apparatuses continue toseek improved bearing assembly and apparatus designs and manufacturingtechniques.

SUMMARY

Various embodiments of the invention relate to bearing assemblies andapparatuses that may include a support ring to which one or moresuperhard bearing elements may be secured. The support ring may includeone or more relief features configured to reduce residual stressesformed in the superhard bearing elements by brazing the superhardbearing elements to the support ring, operational loads, or otherprocesses. The various embodiments of the bearing assemblies andapparatuses may be used in subterranean drilling systems and/or othertypes of systems.

In an embodiment, a bearing assembly for use in a subterranean drillingsystem may include a plurality of superhard bearing elements and asupport ring. The support ring may include a plurality of recessesdistributed circumferentially about a rotation axis. A corresponding oneof the plurality of superhard bearing elements may be affixed to thesupport ring in a corresponding one of the plurality of recesses. Thebearing assembly may also include a plurality of relief features formedin the support ring. Each of the plurality of relief features may bedisposed between adjacent recesses of the plurality of recesses. In anembodiment, the plurality of relief features may be configured to reduceresidual stresses in the plurality of superhard bearing elements causedby securing (e.g., brazing) the plurality of superhard bearing elementsto the support ring.

In an embodiment, a bearing apparatus for use in a subterranean drillingsystem may include a first bearing assembly and a second bearingassembly. The first bearing assembly may include a plurality of firstsuperhard bearing elements each of which may include a first bearingsurface. The first bearing assembly may also include a support ring thatmay include a plurality of recesses distributed circumferentially abouta rotation axis. A corresponding one of the plurality of first superhardbearing elements may be affixed to the support ring in a correspondingone of the plurality of recesses. The support ring may also include aplurality of relief features formed in the support ring. Each of theplurality of relief features may be disposed between adjacent recessesof the plurality of recesses. The second bearing assembly may include aplurality of second superhard bearing elements each of which may includea second bearing surface generally opposing the first bearing surfacesof the plurality of first superhard bearing elements. In an embodiment,the plurality of relief features may be configured to reduce residualstresses in the plurality of first superhard bearing elements caused bysecuring (e.g., brazing) the plurality of first superhard bearingelements to the support ring.

In an embodiment, a method for manufacturing a bearing assembly for usein a subterranean drilling system may include providing a support ring.The support ring may include a plurality of recesses distributedcircumferentially about an axis. The support ring may also include aplurality of relief features formed in the support ring, and each of therelief features may be disposed between adjacent recesses of theplurality of recesses. The plurality of superhard bearing elements maybe brazed to the support ring without forming cracks in at least aportion of the plurality of superhard bearing elements that extendgenerally perpendicular to the axis.

Other embodiments include applications utilizing the disclosed bearingassemblies in various types of drilling systems and other applications.

Features from any of the disclosed embodiments may be used incombination with one another, without limitation. In addition, otherfeatures and advantages of the present disclosure will become apparentto those of ordinary skill in the art through consideration of thefollowing detailed description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate several embodiments of the invention, whereinidentical reference numerals refer to identical elements or features indifferent views or embodiments shown in the drawings.

FIG. 1A is an isometric view of a radial bearing assembly according toan embodiment;

FIG. 1B is an isometric view of the radial bearing assembly shown inFIG. 1A with the superhard bearing elements removed;

FIG. 1C is a cross-sectional view of the support ring shown in FIG. 1B;

FIGS. 2A-2C are partial isometric views of radial bearing assembliesaccording to other embodiments;

FIG. 3 is an isometric cutaway view of a radial bearing apparatusaccording to an embodiment;

FIG. 4 is an isometric view of a thrust-bearing assembly according to anembodiment;

FIG. 5 is an isometric cutaway view of a thrust-bearing apparatus thatmay utilize any of the disclosed thrust-bearing assemblies according toan embodiment;

FIG. 6A is an isometric cutaway view of an angular contact bearingapparatus according to an embodiment;

FIG. 6B is a partial cross-sectional view taken along line 6B-6B of theangular contact bearing apparatus shown in FIG. 6A; and

FIG. 7 is a schematic isometric cutaway view of a subterranean drillingsystem including a thrust-bearing apparatus utilizing any of thedescribed bearing assemblies according to various embodiments.

DETAILED DESCRIPTION

Embodiments of the invention relate to bearing assemblies, bearingapparatuses, and motor assemblies that include support rings havingrelief features configured to prolong the useful life of superhardbearing elements secured to the support rings. FIG. 1A is an isometricview of a radial bearing assembly 100 according to an embodiment. Theradial bearing assembly 100 may form a stator or a rotor of a radialbearing apparatus used in a subterranean drilling system, a pump, aturbine, and/or other types of systems. The radial bearing assembly 100may include a support ring 102 defining an opening 104 through which ashaft or spindle (not shown) of, for example, a drilling motor mayextend. The support ring 102 may be made from a variety of differentmaterials. For example, the support ring 102 may comprise carbon steel,stainless steel, tungsten carbide, or another suitable material.

The radial bearing assembly 100 further may include a plurality ofsuperhard bearing elements 106. The plurality of superhard bearingelements 106 may be distributed about a rotation axis 108 incorresponding recesses 110 (see FIG. 1B) formed in the support ring 102and arranged in a first row and a second row. In other embodiments, thesuperhard bearing elements 106 may be circumferentially distributedabout the axis 108 in a single row, three rows, or any number of rows.The superhard bearing elements 106 may be generally cylindrical,generally non-cylindrical, generally rectangular, generally wedgeshaped, or any other suitable configuration.

Some or all of the superhard bearing elements 106 may comprise asuperhard table 112 including a convexly-curved bearing surface 114(e.g., curved to lie on an imaginary cylindrical surface). In otherembodiments, the bearing surfaces 114 may be concavely-curved or haveother suitable shapes. Each superhard table 112 may be bonded orattached to a corresponding substrate 116. A portion of or all of thesuperhard bearing elements 106 may be partially secured in the recesses110 via brazing, welding, soldering, press-fitting, fastening with afastener, or another suitable technique. As used herein a “superhardbearing element” is a bearing element including a bearing surface thatis made from a material exhibiting a hardness that is at least as hardas tungsten carbide.

In any of the embodiments disclosed herein, the superhard bearingelements 106 may be made from one or more superhard materials, such aspolycrystalline diamond, polycrystalline cubic boron nitride, siliconcarbide, tungsten carbide, or any combination of the foregoing superhardmaterials. For example, the superhard table may be formed frompolycrystalline diamond and the substrate may be formed fromcobalt-cemented tungsten carbide. Furthermore, in any of the embodimentsdisclosed herein, the polycrystalline diamond table may be leached to atleast partially or substantially completely remove a metal-solventcatalyst (e.g., cobalt, iron, nickel, or alloys thereof) that was usedto initially sinter precursor diamond particles that form thepolycrystalline diamond. In another embodiment, an infiltrant used tore-infiltrate a preformed leached polycrystalline diamond table may beleached or otherwise removed to a selected depth from a bearing surface.Moreover, in any of the embodiments disclosed herein, thepolycrystalline diamond may be unleached and include a metal-solventcatalyst (e.g., cobalt, iron, nickel, or alloys thereof) that was usedto initially sinter the precursor diamond particles that form thepolycrystalline diamond or an infiltrant used to re-infiltrate apreformed leached polycrystalline diamond table. Other examples ofmethods for fabricating the superhard bearing elements are disclosed inU.S. Pat. Nos. 7,866,418, 7,842,111; and co-pending U.S. patentapplication Ser. No. 11/545,929, the disclosure of each of which isincorporated herein, in its entirety, by this reference.

The diamond particles that may form the polycrystalline diamond in thesuperhard table 112 may also exhibit a larger size and at least onerelatively smaller size. As used herein, the phrases “relatively larger”and “relatively smaller” refer to particle sizes (by any suitablemethod) that differ by at least a factor of two (e.g., 30 μm and 15 μm).According to various embodiments, the diamond particles may include aportion exhibiting a relatively larger size (e.g., 30 μm, 20 μm, 15 μm,12 μm, 10 μm, 8 μm) and another portion exhibiting at least onerelatively smaller size (e.g., 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, 0.5μm, less than 0.5 μm, 0.1 μm, less than 0.1 μm). In an embodiment, thediamond particles may include a portion exhibiting a relatively largersize between about 10 μm and about 40 μm and another portion exhibitinga relatively smaller size between about 1 μm and 4 μm. In someembodiments, the diamond particles may comprise three or more differentsizes (e.g., one relatively larger size and two or more relativelysmaller sizes), without limitation.

Additionally, in any of the embodiments disclosed herein, the superhardbearing elements 106 may be free-standing (e.g., substrateless) andformed from a polycrystalline diamond body that is at least partially orfully leached to remove a metal-solvent catalyst initially used tosinter the polycrystalline diamond body.

In the illustrated embodiment, the support ring 102 may include relieffeatures (e.g., stress-relief features) configured to reduce residualstresses including compressive hoop stresses, tensile axial stresses,combinations thereof, and the like that may be induced in the superhardbearing elements 106 by securing the superhard bearing elements 106 tothe support ring 102 by brazing or other method, operational loads,other processes, or combinations of the foregoing. For example, thesuperhard bearing elements 106 may be secured to the support ring 102via a thermal process such as brazing. Brazing may cause the recesses110 of the support ring 102 to expand and contract relative to thesuperhard bearing elements 106 because the support ring 102 generallyhas a coefficient of thermal expansion greater than that of thesuperhard bearing elements 106. When the recesses 110 contract, therecesses 110 of the support ring 102 may place compressive hoop stressesσ₂ on the superhard bearing elements 106. These compressive hoopstresses σ₂ may generate residual stresses in the superhard bearingelements 106 that can give rise to damage (e.g., tensile fracture) onthe superhard bearing elements 106. More specifically, as shown in FIG.1A, residual compressive hoop stresses σ₂ may induce axial tensilestresses σ₁ in the superhard bearing elements 106 that may damage thesuperhard bearing elements 106. Operational loads (not shown) may alsoadd to the residual stresses within the superhard bearing elements 106and cause failure that would otherwise not have occurred.

In an embodiment, one or more grooves 118 may be formed in the supportring 102 between adjacent (e.g., immediately adjacent) ones of thesuperhard bearing elements 106 and the recesses 110. The grooves 118 maybe configured to help reduce the residual stresses in the superhardbearing elements 106 as a result of brazing the superhard bearingelements 106 to the support ring 102, operational loads, otherprocesses, or combinations thereof. The grooves 118 may be configured toreduce the residual stresses in the superhard bearing elements 106 byfunctioning to at least partially segment the support ring 102 betweenthe recesses 110 to lessen the clamping pressure on the superhardbearing elements 106 by making the support ring 102 more compliant(i.e., less stiff) in a circumferential direction. In other embodiments,the grooves 118 may be configured to reduce brazing-induced stresses inthe superhard bearing elements 106 by functioning asexpansion/contraction joints between the recesses 110 to compensate forthermal expansion and/or contraction of the recesses 110 relative to thesuperhard bearing elements 106. In yet other embodiments, the grooves118 may be configured to function as heat dissipaters to attract energyin the form of heat away from the recesses 110 and the superhard bearingelements 106. More specifically, the grooves 118 may provide a largerheat dissipation surface area between the recesses 110 such that thetemperature rise of the support ring 102 between the recesses 110 due tobrazing, during use, or other processes is lower.

By reducing the residual stresses in the superhard bearing elements 106,the grooves 118 may reduce fracturing on the superhard bearing elements106 and may advantageously help prolong the useful life of the superhardbearing elements 106.

As shown in FIGS. 1A and 1B, the grooves 118 may have a generallysemi-cylindrical shape. While the grooves 118 are illustrated having agenerally semi-cylindrical shape, the grooves 118 may have a generallyrectangular shape, a generally crescent shape, a generally diamondshape, combinations thereof, or any other shape suitable to help reducestresses in the superhard bearing elements 106. In the illustratedembodiment, the grooves 118 may have substantially the sameconfiguration and shape. In other embodiments, the grooves 118 may haveconfigurations and/or shapes that vary from one groove 118 to anothergroove 118. For example, a first one of the grooves 118 may have agenerally diamond shape, a second one of the grooves 118 may have agenerally semi-cylindrical shape, and a third one of the grooves 118 mayhave a generally rectangular shape.

Each of the grooves 118 may have a maximum length L as shown in FIG. 1A.The maximum length L of one or more of the grooves 118 may extendbetween opposite end portions of the grooves 118. In an embodiment, themaximum length L of at least one of the grooves 118 may be about 0.3inches to about 1.5 inches, such as about 0.5 inches to about 0.8inches. However, in other embodiments, the maximum length L of at leastone of the grooves 118 may be longer or shorter than the foregoingranges for the maximum length L. As illustrated, each of the grooves 118may have at least substantially the same maximum length L. However, inother embodiments, some or all of the grooves 118 may have substantiallydifferent maximum lengths L. For example, in an embodiment, the supportring 102 may include a first group of grooves 118 having maximum lengthsof about 1.2 inches and a second group of grooves 118 having maximumlengths of about 0.6 inches. In some embodiments, at least some of thegrooves 118 may extend to an upper end surface 109 or a lower endsurface 111.

In an embodiment, the relationship between the maximum length L of atleast one the grooves 118 and a maximum width WR of at least one of therecesses (shown in FIG. 1C) may be configured to help reduce thestiffness of the support ring 102 during brazing and/or use. Increasingthe maximum length L of the grooves 118 relative to the maximum width WRof the recesses 110 may increase the heat exchange surface between thegrooves 118 and the recesses 110 and/or create greaterexpansion/contraction joints in the grooves 118 for the recesses 110.For example, the maximum length L of at least one of the grooves 118 maybe at least: about ninety (90) percent; about one hundred (100) percent;about one hundred and ten (110) percent; about one hundred and twenty(120) percent; about one hundred and thirty (130) percent; about onehundred and forty (140) percent; or about one hundred and fifty (150)percent of the maximum width WR of the recesses 110. In otherembodiments, the maximum length L of the grooves 118 may be about onehundred (100) percent to about one hundred and forty (140) percent;about one hundred and ten (110) percent to about one hundred and thirty(130) percent; or at least about one hundred and twenty (120) percent ofthe maximum width WR of at least one of the recesses 110. In otherembodiments, the maximum length L of at least one of the grooves 118 andthe maximum width WR of at least one of the recesses 110 may be largeror smaller relative to each other.

Similar to the relationship between the maximum length L of the grooves118 and the maximum width WR of the recesses 110, the relationshipbetween the maximum length L of at least one of the grooves 118 and amaximum width WS of at least one of the superhard bearing elements 106(shown in FIG. 1A) may be configured to help reduce the residualstresses in the superhard bearing elements 106 that are brazed intosupport ring 102. For example, the maximum length L of at least one ofthe grooves 118 may be at least: about ninety (90) percent; about onehundred (100) percent; about one hundred and ten (110) percent; aboutone hundred and twenty (120) percent; about one hundred and thirty (130)percent; about one hundred and forty (140) percent; and/or about onehundred and fifty (150) percent of the maximum width WS of at least oneof the superhard bearing elements 106. In other embodiments, the maximumlength L of at least one of the grooves 118 may be between about onehundred (100) percent and about one hundred and forty (140) percent; orbetween about one hundred and ten (110) percent and about one hundredand thirty (130) percent, and/or about one hundred and twenty (120)percent of the maximum width WS of at least one of the superhard bearingelements 106. In other embodiments, the maximum length L of at least oneof the grooves 118 and the maximum width WS of at least one of thesuperhard bearing elements 106 may be larger or smaller relative to eachother.

Referring now to FIG. 1C, each of the grooves 118 may also include amaximum depth D and a maximum width W. Generally, the maximum depth Dmay extend only partially through the support ring 102 or completelythrough the support ring 102. For example, the maximum depth D may beabout 0.1 inches to about 0.4 inches, such as about 0.15 inches to about0.25 inches. Variations of the maximum depth D and/or the maximum widthW of the grooves 118 may help the grooves 118 function as heatdissipaters, expansion/contraction joints, and/or to segment the supportring 102 to help reduce the stiffness and/or displacement of the supportring 102 during brazing and/or use.

As illustrated, the grooves 118 may be formed in a section of a wall 120of the support ring 102. The wall 120 may have a thickness T thatextends between an outer surface 122 and an inner surface 124. Themaximum depth D of the grooves 118 may extend between the outer surface122 of the wall 120 and a lower surface within the grooves 118, or thegrooves 118 may extend completely through the wall 120 (i.e., throughslots or grooves). As illustrated, the grooves 118 may have at leastsubstantially the same maximum depth D. However, in other embodiments,some or all of the grooves 118 may have substantially different maximumdepths D. In addition, the maximum depths D of the grooves 118 may vary.For example, at least one of the grooves 118 may have a maximum depth Dthat includes a deeper portion and a shallower portion.

In an embodiment, the relationship between the maximum depth D of atleast one of the grooves 118 and the thickness T of the wall 120 may beconfigured to help reduce the residual stresses in the superhard bearingelements 106. For example, the maximum depth D of at least one of thegrooves 118 may be about thirty (30) percent to about ninety (90)percent; about forty (40) percent to about eighty (80) percent; aboutfifty (50) percent to seventy (70) percent; about fifty-five (55)percent to about sixty-five (65) percent of the thickness T of the wall120. In another embodiment, the depth D of at least one of the grooves118 may be at least about forty (40) percent, at least about fifty (50)percent, at least about sixty (60) percent, about seventy (70) percent,or at least about eighty (80) percent of the thickness T of the wall120. In other embodiments, the maximum depth D of the grooves 118 andthe thickness T of the wall 120 may be larger or smaller relative toeach other. For example, in an embodiment, the maximum depth D of thegrooves 118 may extend entirely through the thickness T of the wall 120.

As shown in FIG. 1C, the maximum width W of each of the grooves mayextend between opposing sidewalls of the grooves 118. In an embodiment,the maximum width W of at least one of the grooves 118 may be about 0.1inches to about 0.3 inches, such as about 0.125 inches to about 0.2inches. In other embodiments, the maximum widths W of at least one ofthe grooves 118 may be wider or narrower. As illustrated, the grooves118 may have at least substantially the same maximum widths W. However,in other embodiments, some or all of the grooves 118 may havesubstantially different maximum widths W. In addition, the maximumwidths W of the grooves 118 may vary. For example, at least one of thegrooves 118 may have a maximum width W that includes a narrower portionand a wider portion.

In an embodiment, the relationship between the maximum width W of atleast one of the grooves 118 and the maximum width WR of at least one ofthe recesses 110 may be configured to help reduce the stiffness and/ordisplacement of the support ring 102 during brazing or use. For example,the maximum width W of at least one of the grooves 118 may be at least:about ten (10) percent; about fifteen (15) percent; about twenty (20)percent; about twenty-five (25) percent; or about thirty (30) percent ofthe WR of the recesses 110. In addition, the maximum width of grooves118 may be about ten (10) percent to about thirty (30) percent; or aboutfifteen (15) percent to about twenty-five (25) percent; or at leastabout twenty (20) percent of the maximum width WR of the recesses 110.In other embodiments, the maximum widths W of the grooves 118 and themaximum widths WR of the recesses 110 may be larger or smaller relativeto each other.

In an embodiment, the relationship between the maximum width W of atleast one of the grooves 118 and the maximum width WS of at least one ofthe superhard bearing elements 106 may be configured to help reduce theresidual stresses due to brazing of the superhard bearing elements 106into the support ring 102. For example, the maximum width W of at leastone of the grooves 118 may be at least: about ten (10) percent; aboutfifteen (15) percent; about twenty (20) percent; about twenty-five (25)percent; or about thirty (30) percent of the maximum width WS of thesuperhard bearing elements 106. In addition, the maximum width W of atleast one of the grooves 118 may be: about ten (10) percent to aboutthirty (30) percent; about fifteen (15) percent to about twenty-five(25) percent; or at least about twenty (20) percent of the maximum widthWS of the superhard bearing elements 106. In other embodiments, themaximum widths W of the grooves 118 and the maximum widths WS of thesuperhard bearing elements 106 may be larger or smaller relative to eachother.

In an embodiment, the relationship between the maximum length L and themaximum depth D of at least one of the grooves 118 may be configured tohelp reduce the stiffness or displacement of the support ring 102 duringbrazing or use. For example, the maximum length of at least one of thegrooves 118 may be at least: about one hundred (100) percent; about twohundred (200) percent; about three hundred (300) percent; about fourhundred (400) percent; about five hundred (500) percent; about sixhundred (600) percent; about seven hundred (700) percent; or about eighthundred (800) percent of the maximum depth D of the groove 118. Inaddition, the maximum length L of at least one of the grooves 118 maybe: about four hundred (400) percent to eight hundred (800) percent; orabout five hundred (500) percent to seven hundred (700) percent of themaximum depth of the grooves 118; or about six hundred (600) percent ofthe maximum depth D of the groove 118. In other embodiments, the maximumdepths D and the maximum lengths L of the grooves 118 may be larger orsmaller relative to each other.

In an embodiment, the relationship between the maximum length L and themaximum width W of at least one of the grooves 118 may be configured tohelp reduce the stiffness or displacement of the support ring 102 duringbrazing or use. For example, the maximum length L of at least one of thegrooves 118 may be at least: about one hundred (100) percent; about twohundred (200) percent; about three hundred (300) percent; about fourhundred (400) percent; about five hundred (500) percent; about sixhundred (600) percent; about seven hundred (700) percent; or about eighthundred (800) percent of the maximum width W. In addition, the maximumlength L of at least one of the grooves 118 may be: about four hundred(400) percent to about eight hundred (800) percent; or about fivehundred (500) percent to about seven hundred (700) percent; or at leastabout six hundred (600) percent of the maximum width W of the groove118. In other embodiments, the maximum widths W and the maximum lengthsL of the grooves 118 may be larger or smaller relative to each other.

In an embodiment, the relationship between the maximum depth D and themaximum width W of at least one of the grooves 118 may be configured tohelp reduce the stiffness or displacement of the support ring 102 duringbrazing or use. For example, the maximum depth D of at least one of thegrooves 118 may be at least: about fifty (50) percent; about one hundred(100) percent; about one hundred and fifty (150) percent; about twohundred (200) percent; or about three hundred (300) percent of themaximum width W of the groove 118. In addition, the maximum depth D ofat least one of the grooves 118 may be about fifty (50) percent to aboutone hundred and fifty (150) percent; or about one hundred (100) percentof the maximum width W the groove 118. In other configurations, themaximum depths D and the maximum widths W of the grooves 118 may belarger or smaller relative to each other.

Referring now to FIG. 1B, the grooves 118 may be disposed betweenadjacent (e.g., immediately adjacent) ones of the recesses 110 of thesupport ring 102. As shown, each of the grooves 118 may be disposedequidistantly between adjacent ones of the recesses 110 of the supportring 102. In other embodiments, the grooves 118 may be disposed closerto one of adjacent ones of the recesses 110. In other embodiments, twoor more grooves 118 may be disposed between adjacent ones of therecesses 110. The grooves 118 may also be disposed between only some ofthe recesses 110. For example, the grooves 118 may be located betweenevery other pair of adjacent ones of the recesses 110 of the supportring 102 or in any other configuration around the axis 108. The grooves118 may also be positioned in various locations on the support ring 102.For example, the grooves 118 may be located above and/or below therecesses 110.

In an embodiment, the radial bearing assembly 100 may be manufactured byforming the recesses 110 and grooves 118 in the support ring 102. Inother embodiments, the support ring 102 may be provided with therecesses 110 and/or the grooves 118 already formed therein. Thus, thisstep may be omitted. One or more filler metals may be placed in therecesses 110. The one or more filler metals may include brazing filleralloys or other suitable material. For example, one suitable brazingfiller alloy is an alloy of about 50.0 weight % (“wt %”) silver, about20.0 wt % copper, about 28.0 wt % zinc, and about 2.0 wt % nickel,otherwise known as Braze 505 from Lucas-Milhaupt. Other suitable brazingfiller alloys may include, but are not limited to, an alloy of about 4.5wt % titanium, about 26.7 wt % copper, and about 68.8 wt % silver,otherwise known as TICUSIL®, and an alloy of about 25 wt % silver, about37 wt % copper, about 10 wt % nickel, about 15 wt % palladium, and about13 wt % manganese, otherwise known as PALNICUROM® 10. Both of theTICUSIL® and PALNICUROM® 10braze alloys are currently commerciallyavailable from Wesgo Metals, Hayward, Calif.

The superhard bearing elements 106 may then be placed in the recesses110 containing the one or more filler metals. The one or more fillermetals, the superhard bearing elements 106, and the support ring 102including the recesses 110 may then be subjected to a thermal process tobring the one or more filler metals slightly above their liquidustemperature (i.e., melting temperature) such that the one or more fillermetals flow between the superhard bearing elements 106 and the recesses110. The thermal process may include brazing, soldering, welding, or anyother suitable thermal process. The one or more filler metals may thenbe cooled to solidify and join the superhard bearing element 106 and therecess 110 together, thereby securing the superhard bearing elements 106to the support ring 102 with no or little fracturing of the superhardbearing elements 106. During the thermal process, the grooves 118 mayhelp prevent damage to the superhard bearing elements 106 by functioningas expansion/contraction joints to help reduce any thermal expansionand/or contraction of the recesses 110. The grooves 118 may also helpprevent damage of the superhard bearing elements 106 by reducing thestiffness of the support ring 102 during brazing or during use.

Any of the bearing assembly or bearing apparatus embodimentscontemplated by the present invention may be manufactured according tothe above described methods or similar methods.

FIGS. 2A-2C are partial isometric views of radial bearing assembliesaccording to other embodiments. The radial bearing assemblies shown inFIGS. 2A-2C are similar in many respects to the radial bearing assembly100 except for the configuration of the grooves 118. For ease ofdescription, only the upper portions of the radial bearing assembliesare illustrated. As shown in FIG. 2A, radial bearing assembly 100A mayinclude the support ring 102. The support ring 102 may include recesses110 and grooves 118 having a generally hourglass shape. Each of thegrooves 118 may be located between adjacent ones of the recesses 110.The hourglass shape of the grooves 118 may help reduce stresses formedin the superhard bearing elements 106 (shown in FIG. 1A) because agreater portion of the support ring 102 is removed between the recesses110. The hourglass grooves 118 may also have a relatively large heatdissipation surface area.

In another embodiment, radial bearing assembly 100B may include thesupport ring 102. The support ring 102 may include recesses 110 andgrooves 118 having a generally crescent shape as illustrated in FIG. 2BLike the embodiment shown in FIG. 2A, each of the grooves 118 may belocated between adjacent ones of the recesses 110. The generallycrescent grooves 118 may be located above, below, and/or between therecesses 110. The generally crescent shape of the grooves 118 may helpreduce brazing stresses formed in the superhard bearing elements 106 byallowing the grooves 118 to extend around a portion of a perimeter ofthe recesses 110. Hence, the generally crescent grooves 118 mayeffectively decrease the stiffness of the support ring 102 and/orprovide expansion/contraction joints between the recesses 110 that atleast partially encompass the recesses 110.

In yet another embodiment, radial bearing assembly 100C may include thesupport ring 102. The support ring 102 may include the grooves 118located between every other adjacent ones of the recesses 110 as shownin FIG. 2C. In other embodiments, the grooves 118 may be located betweenevery third adjacent ones of the recesses 110 or a pair of grooves 118may be located between adjacent ones of the recesses 110. In yet otherembodiments, two or more grooves 118 may be located between adjacentones of the recesses 110. Varying the location of the grooves 118 on thesupport ring 102 may help to selectively tailor forces, loads, stresses,or combinations thereof within the support ring 102.

Any of the above-described radial bearing assembly embodiments may beemployed in a radial bearing apparatus. FIG. 3 is an isometric cutawayview of a radial bearing apparatus 300. The radial bearing apparatus 300may include an inner race 326 (i.e., stator) configured as any of thepreviously described embodiments of radial bearing assemblies or anyother radial bearing assemblies contemplated by the present invention.In an embodiment, the inner race 326 may define an opening 328. Theinner race 326 may include a support ring 330 and a plurality ofsuperhard bearing elements 332 distributed circumferentially about arotation axis 308 in corresponding recesses 336 formed in the supportring 330. As shown, the recesses 336 may be arranged in a first row anda second row. In other embodiments, the recesses 336 may becircumferentially distributed in a single row, three rows, or any numberof rows. Each of the superhard bearing elements 332 may include aconvexly-curved bearing surface 334. The superhard bearing elements 332may be made from any of the materials discussed above for the superhardbearing elements 106. One or more grooves (not shown) may be formed inthe support ring 330 between adjacent ones of the superhard bearingelements 332 and/or the recesses 336. The grooves may be configuredsimilar to the grooves 118 shown in FIGS. 1A-1C or any other groovecontemplated by the present invention.

The radial bearing apparatus 300 may further include an outer race 338(i.e., a rotor) that extends about and receives the inner race 326. Theouter race 338 may include a support ring 340 and a plurality ofsuperhard bearing elements 342 mounted or otherwise attached to thesupport ring 340. Each of the plurality of circumferentially-distributedsuperhard bearing elements 342 may include a concavely-curved bearingsurface 344 curved to correspond to the convexly-curved bearing surfaces334. The superhard bearing elements 342 may be made from any of thematerials discussed above for the superhard bearing elements 106. Theouter race 338 may also include recesses 346 formed in the support ring340 that correspond to first and second rows of recesses 336 in thesupport ring 330 of the inner race 326. One or more grooves (not shown)may be formed in the support ring 340 between adjacent ones of thesuperhard bearing elements 342 and/or the recesses 346. The grooves maybe configured similar to the grooves 118 shown in FIGS. 1A-1C or anyother groove disclosed herein.

The terms “rotor” and “stator” refer to rotating and stationarycomponents of the radial bearing apparatus 300, respectively. Thus, ifthe outer race 338 is configured to remain stationary, the outer race338 may be referred to as the stator and the inner race 326 may bereferred to as the rotor. One will appreciate that the radial bearingapparatus 300 may be employed in a variety of mechanical applications.For example, drill bits, pumps or turbines may benefit from a radialbearing apparatus disclosed herein.

The concepts used in the radial bearing assemblies and apparatusesdescribed above may also be employed in thrust-bearing assemblies andapparatuses. FIG. 4 is an isometric view of a thrust-bearing assembly400 according to an embodiment. The thrust-bearing assembly 400 may forma stator or a rotor of a thrust-bearing apparatus used in a subterraneandrilling system. As shown in FIG. 4, the thrust-bearing assembly 400 mayinclude a support ring 402 defining an outer surface 426 and an opening424 through which a shaft (not shown) of, for example, a downholedrilling motor may extend. The support ring 402 may be made from avariety of different materials such as carbon steel, stainless steel,tungsten carbide, combinations thereof, or another suitable material.The thrust-bearing assembly 400 further may include a plurality ofsuperhard bearing elements 406 and a plurality of recesses (not shown)formed in the support ring 402. The superhard bearing elements 406 maybe partially disposed in a corresponding one of the recesses of thesupport ring 402 and secured partially therein via brazing,press-fitting, or another suitable technique.

The superhard bearing elements 406 are illustrated being distributedcircumferentially about a thrust axis 408 along which a thrust force maybe generally directed during use. Some of or all of the superhardbearing elements 406 may comprise a superhard table 412 including abearing surface 414. Each superhard table 412 may be bonded or attachedto a corresponding substrate 416. The superhard bearing elements 406 mayeach be made from any of the materials discussed above for the superhardbearing elements 106.

In the illustrated embodiment, the support ring 402 may also includerelief features configured to help reduce the stiffness (i.e., increasecompliance) of the support ring 402 during brazing or use. For example,the relief features may be configured to help reduce the compressivehoop stresses, the axial tensile stresses, other stresses, orcombinations thereof formed in the superhard bearing elements 406 as aresult of brazing the superhard bearing elements 406 to the support ring402, operational loads, and/or other processes. In an embodiment, one ormore grooves 418 may be formed in the support ring 402 between adjacentones of the superhard bearing elements 406 and the recesses. The grooves418 may be configured similar to grooves 118 or those described inrelation to FIGS. 2A-2C, or any other groove contemplated by the presentinvention.

The grooves 418 may be configured to at least partially reduce thestiffness of the support ring 402, act as expansion/contraction jointsbetween the recesses, act as heat dissipaters to draw energy away fromthe recesses, and the like. In an embodiment, the grooves 418 may have agenerally semi-cylindrical shape. In other embodiments, the grooves 418may have a generally rectangular shape, a generally crescent shape, agenerally hourglass shape, a generally diamond shape, combinationsthereof, or any other shape suitable to, for example, help reducestresses in the superhard bearing elements 406.

In an embodiment, the grooves 418 may have substantially the sameconfiguration and shape. In other embodiments, the grooves 418 may haveconfigurations and/or shapes that vary from one groove 418 to anothergroove 418. For example, the grooves 418 may include a first group ofgrooves 418 having generally semi-cylindrical shapes and a second groupof grooves 418 having generally hourglass shapes.

Referring still to FIG. 4, the grooves 418 may be positioned betweeneach of the superhard bearing elements 406 of the support ring 402. Inan embodiment, the grooves 418 may be located about equidistant betweenadjacent ones of the superhard bearing elements 406 of the support ring402 or closer to one of the adjacent ones of the superhard bearingelements 406. In other embodiments, the grooves 418 may be positioned inother locations on the support ring 402. For example, the grooves 418may be located above the superhard bearing elements 406, below thesuperhard bearing elements 406, and/or at any other suitable location onthe support ring 402 to help reduce stresses in the superhard bearingelements 406. In addition, while a groove 418 is illustrated betweeneach of the superhard bearing elements 406, the grooves 418 may bepositioned between a selected some of the superhard bearing elements406. For example, the grooves 418 may be absent between some of theadjacent ones of the superhard bearing elements 406 and included betweenothers of the adjacent ones of the superhard bearing elements 406. Inother embodiments, one or more of the grooves 418 may be disposedbetween every other pair of adjacent ones of the superhard bearingelements 406.

Any of the above-described thrust-bearing assembly embodiments may beemployed in a thrust-bearing apparatus. FIG. 5 is a partial isometriccutaway view of a thrust-bearing apparatus 500. The thrust-bearingapparatus 500 may include a stator 526 configured as any of thepreviously described embodiments of thrust-bearing assemblies. Thestator 526 may include a plurality of circumferentially-adjacentsuperhard bearing elements 532. At least some of or all of the superhardbearing elements 532 may include a bearing surface 534 and may exhibit,for example, the configuration described herein above relative to thesuperhard bearing elements 106. The superhard bearing element 532 may bemounted or otherwise attached to a support ring 530 in recesses (notshown). The support ring 530 may include grooves 548 formed betweenadjacent ones of the superhard bearing elements 532 and recesses. Thegrooves 548 may be configured as described herein above relative to thegrooves 118 shown in FIGS. 1A-1C or any other groove contemplated by thepresent invention.

The thrust-bearing apparatus 500 may also include a rotor 538. The rotor538 may include a support ring 540 having a plurality of recesses 546and a plurality of superhard bearing elements 542, with each of thesuperhard bearing elements 542 having a bearing surface 544. A portionof or all of the superhard bearing elements 542 may be partiallydisposed in a corresponding one of the recesses 546 of the support ring540 and secured partially therein via brazing or other suitabletechniques. One or more grooves (not shown) may be formed in the supportring 540 between adjacent ones of the superhard bearing elements 542.The grooves of the support ring 540 may be configured similar to thegrooves 118 shown in FIGS. 1A-1C or any other groove disclosed herein.As shown, a shaft 552 may be coupled to the support ring 540 andoperably coupled to an apparatus capable of rotating the shaft 552 indirection R (or in a generally opposite direction), such as a downholemotor. For example, the shaft 552 may extend through and may be securedto the support ring 540 of the rotor 538 by press-fitting or threadlycoupling the shaft 552 to the support ring 540 or another suitabletechnique.

The concepts used in the radial bearing assemblies and apparatuses andthrust-bearing assemblies and apparatuses described above may also beemployed in angular contact bearing assemblies and apparatuses. Forexample, FIGS. 6A and 6B illustrate an angular contact bearing apparatus600 that is configured to carry both radial loads and thrust loads. Inan embodiment, the angular contact bearing apparatus 600 may include aninner race 626 and an outer race 638. The outer race 638 may receive theinner race 626, and the outer race 638 and the inner race 626 may beconfigured to move relative to each other. For example, the inner race626 may be independently rotatable about three mutually orthogonal axesX, Y, and Z (shown in FIG. 6B) and connected to, for example, an outputshaft of a motor and the outer race 638 may be stationary, or viceversa.

The inner race 626 may include a support ring 630 having a plurality ofcircumferentially-adjacent superhard bearing elements 632. The superhardbearing elements 632 may include a convexly-shaped bearing surface 634that generally lies on an imaginary spherical reference surface and maybe oriented to carry thrust and radial loads. The superhard bearingelements 632 may be mounted or otherwise attached to the support ring630 at least partially within recesses 636 formed in the support ring630. The support ring 630 may also include also grooves 648 formedbetween adjacent ones of the superhard bearing elements 632. The grooves648 may be configured as described herein above in relation to thegrooves 118 shown in FIGS. 1A-1C or any other groove disclosed herein.

As shown in FIGS. 6A and 6B, the outer race 638 may include a supportring 640 having a plurality of circumferentially-adjacent superhardbearing elements 642. The superhard bearing elements 642 may include aconcavely-shaped bearing surface 644 that generally lies on an imaginaryspherical reference surface and may be oriented to carry thrust andradial loads. The superhard bearing elements 642 may be mounted orotherwise attached to the support ring 640 at least partially withinrecesses 646 formed in the support ring 640. The support ring 640 mayalso include grooves 650 formed between adjacent ones of the superhardbearing elements 642. The grooves 650 may be configured as describedherein above in relation to the grooves 118 shown in FIGS. 1A-1C or anyother groove contemplated by the present invention.

While the grooves 648 and 650 are illustrated in FIGS. 6A and 6B havinga generally cylindrical shape, the grooves 648 and 650 may have agenerally rectangular shape, a generally crescent shape, a generallyhourglass shape, a generally diamond shape, combinations thereof, or anyother suitable shape to help reduce stresses in the superhard bearingelements 632, 642. In an embodiment, the grooves 648 and 650 may havesubstantially the same configuration and shape. In other embodiments,the grooves 648 and 650 may have configurations and/or shapes that varybetween the grooves 648 and/or the grooves 650. In other embodiments,the grooves 648 and/or the grooves 650 may extend completely through thesupport rings 630 and 640, respectively, or may be located above, below,and or intermittently between the recesses 636, 646, respectively.

Any of the embodiments for bearing apparatuses discussed above may beused in a subterranean drilling system. FIG. 7 is a schematic isometriccutaway view of a subterranean drilling system 700 according to anembodiment. The subterranean drilling system 700 may include a housing760 enclosing a downhole drilling motor 762 (i.e., a motor, turbine, orany other device capable of rotating an output shaft) that may beoperably connected to an output shaft 756. A thrust-bearing apparatus764 may be operably coupled to the downhole drilling motor 762. Thethrust-bearing apparatus 764 may be configured as any of the previouslydescribed thrust-bearing apparatus embodiments. A rotary drill bit 768may be configured to engage a subterranean formation and drill aborehole and may be connected to the output shaft 756. The rotary drillbit 768 is shown as a roller cone bit including a plurality of rollercones 770. However, other embodiments may utilize different types ofrotary drill bits, such as so-called “fixed cutter” drill bits. As theborehole is drilled, pipe sections may be connected to the subterraneandrilling system 700 to form a drill string capable of progressivelydrilling the borehole to a greater depth within the earth.

The thrust-bearing apparatus 764 may include a stator 772 that does notrotate and a rotor 774 that may be attached to the output shaft 756 androtates with the output shaft 756. As discussed above, thethrust-bearing apparatus 764 may be configured as any of the embodimentsdisclosed herein. For example, the stator 772 may include a plurality ofcircumferentially-distributed superhard bearing elements and grooves(not shown). The rotor 774 may include a plurality ofcircumferentially-distributed superhard bearing elements and grooves(not shown). The grooves in the rotor 774 and/or the stator 772 may beconfigured similar to the grooves 118 shown in FIGS. 1A-1C or any othergroove contemplated by the present invention.

Although several of the bearing assemblies and apparatuses describedabove have been discussed in the context of subterranean drillingsystems and applications, in other embodiments, the bearing assembliesand apparatuses disclosed herein are not limited to such use and may beused for many different applications, if desired, without limitation.Thus, such bearing assemblies and apparatuses are not limited for usewith subterranean drilling systems and may be used with variousmechanical systems, without limitation.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments are contemplated. The various aspects andembodiments disclosed herein are for purposes of illustration and arenot intended to be limiting. Additionally, the words “including,”“having,” and variants thereof (e.g., “includes” and “has”) as usedherein, including the claims, shall be open ended and have the samemeaning as the word “comprising” and variants thereof (e.g., “comprise”and “comprises”).

What is claimed is:
 1. A radial bearing assembly for use in asubterranean drilling system, the bearing assembly comprising: aplurality of superhard bearing elements; and a support ring including:an external surface; a plurality of recesses formed in the externalsurface and distributed circumferentially about a rotation axis, whereina corresponding one of the plurality of superhard bearing elements isaffixed to the support ring in a corresponding one of the plurality ofrecesses, wherein each of the plurality of superhard bearing elementsprotrudes from the external surface; and a plurality of relief featuresformed in the support ring, each of the plurality of relief featuresincluding a groove disposed between adjacent recesses of the pluralityof recesses, the groove of at least one of the plurality of a relieffeatures having a maximum depth of thirty (30) percent to ninety (90)percent of a maximum thickness of the support ring.
 2. The radialbearing assembly of claim 1 wherein at least a portion of the pluralityof superhard bearing elements include a plurality of polycrystallinediamond compacts.
 3. The radial bearing assembly of claim 1 wherein thesupport ring exhibits single-piece construction.
 4. The radial bearingassembly of claim 1 wherein the external surface is a radially innermostsurface of the support ring and each of the plurality of superhardbearing elements protrude radially inwardly from the external surface.5. The radial bearing assembly of claim 1 wherein the external surfaceis a radially outermost surface of the support ring and each of theplurality of superhard bearing elements protrude radially outwardly fromthe external surface.
 6. The radial bearing assembly of claim 1 whereinthe external surface is formed from steel.
 7. The radial bearingassembly of claim 1 wherein the plurality of relief features areconfigured to reduce stresses in the plurality of superhard bearingelements.
 8. The radial bearing assembly of claim 1, wherein a maximumwidth of the groove of at least one of the plurality of relief featuresis ten (10) percent to thirty (30) percent of a maximum width of atleast one of the plurality of recesses.
 9. The radial bearing assemblyof claim 1, wherein a maximum length of the groove of at least one ofthe plurality of relief features is at least one hundred and twenty(120) percent of the maximum width of the at least one of the pluralityof recesses.
 10. The radial bearing assembly of claim 1 wherein each ofthe plurality of relief features includes two closed ends that arebounded by the support ring.
 11. The radial bearing assembly of claim 1,wherein the groove of at least one of the plurality of relief featuresexhibits a generally semi-cylindrical shape, a generally rectangularshape, a generally crescent shape, a generally diamond shape, or agenerally hourglass shape.
 12. A radial bearing apparatus for use in asubterranean drilling system, the radial bearing apparatus comprising: afirst radial bearing assembly including: a plurality of first superhardbearing elements each of which includes a first bearing surface; and asupport ring including: an external surface; a plurality of recessesformed in the external surface and distributed circumferentially about arotation axis, wherein a corresponding one of the plurality of firstsuperhard bearing elements is affixed to the support ring in acorresponding one of the plurality of recesses, wherein each of theplurality of first superhard bearing elements protrude from the externalsurface; and a plurality of relief features formed in the support ring,each of the plurality of relief features include a groove disposedbetween adjacent recesses of the plurality of recesses, the groove of atleast one of the plurality of a relief features having a maximum depthof thirty (30) percent to ninety (90) percent of a maximum thickness ofthe support ring; and a second radial bearing assembly including aplurality of second superhard bearing elements each of which includes asecond bearing surface generally opposing the first bearing surfaces ofthe plurality of first superhard bearing elements.
 13. The radialbearing apparatus of claim 12 wherein the plurality of superhard bearingelements include a plurality of polycrystalline diamond compacts. 14.The radial bearing apparatus of claim 12, wherein the support ringexhibits single-piece construction.
 15. The radial bearing apparatus ofclaim 12, wherein the first radial bearing assembly is an inner race,and wherein: the external surface is a radially outermost surface of thesupport ring; and each of the plurality of first superhard bearingelements protrude radially outwardly from the external surface.
 16. Theradial bearing apparatus of claim 12, wherein the first radial bearingassembly is an outer race configured to receive the second radialbearing assembly, and wherein: the external surface is a radiallyinnermost surface of the support ring; and each of the plurality offirst superhard bearing elements protrude radially inwardly from theexternal surface.
 17. The radial bearing apparatus of claim 12, whereinthe external surface is formed from steel.
 18. The radial bearingapparatus of claim 12, wherein the plurality of relief features areconfigured to reduce stresses in the plurality of superhard bearingelements.
 19. The radial bearing apparatus of claim 12, wherein theplurality of relief features include two closed ends that are bounded bythe support ring.
 20. The radial bearing apparatus of claim 12, whereinthe groove of at least one of the plurality of relief features exhibitsa generally semi-cylindrical shape, a generally rectangular shape, agenerally crescent shape, a generally diamond shape, or a generallyhourglass shape.
 21. A subterranean drilling system, comprising: amotor; a radial bearing apparatus coupled to the motor, the radialbearing apparatus including a radial rotor bearing assembly and a radialstator bearing assembly; wherein one of the radial rotor bearingassembly or the radial stator bearing assembly includes: a plurality offirst superhard bearing elements each of which includes a first bearingsurface; and a support ring including: an external surface; a pluralityof recesses formed in the external surface and distributedcircumferentially about a rotation axis, wherein a corresponding one ofthe plurality of first superhard bearing elements is affixed to thesupport ring in a corresponding one of the plurality of recesses,wherein each of the plurality of first superhard bearing elementsprotrude from the external surface; and a plurality of relief featuresformed in the support ring, each of the plurality of relief featuresincluding a groove disposed between adjacent recesses of the pluralityof recesses, the groove of at least one of the plurality of a relieffeatures having a maximum depth of thirty (30) percent to ninety (90)percent of a maximum thickness of the support ring; and wherein theother of the radial rotor bearing assembly or the radial stator bearingassembly includes a plurality of second superhard bearing elements eachof which includes a second bearing surface generally opposing the firstbearing surfaces of the plurality of first superhard bearing elements.22. The subterranean drilling system of claim 21, wherein the groove ofat least one of the plurality of relief features exhibits a generallysemi-cylindrical shape, a generally rectangular shape, a generallycrescent shape, a generally diamond shape, or a generally hourglassshape.